Efficient quantum pseudorandomness with simple graph states

TL;DR

This paper demonstrates that simple, regular graph states used in measurement-based quantum computation can efficiently generate approximate t-designs, providing a practical approach to quantum pseudorandomness without complex corrections.

Contribution

It introduces a method to produce approximate t-designs using simple, fixed-angle measurements on regular graph states in measurement-based quantum computing.

Findings

Efficient generation of approximate t-designs from simple graph states.

No feed-forward corrections needed for the random unitary ensembles.

Regular graph states serve as universal resources for measurement-based quantum computing.

Abstract

Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements leads to the generation of ensembles of random unitaries, where each random unitary is identified with a string of possible measurement results. We show that repeating an MB scheme an efficient number of times, on a simple graph state, with measurements at fixed angles and no feed-forward corrections, produces a random unitary ensemble that is an {\epsilon}-approximate t-design on n-qubits. Unlike previous constructions, the graph is regular and is also a universal resource for measurement based quantum computing, closely related to the brickwork state